# How to Calculate the Fair Market Price of a Bond Yield to Maturity

When you buy a bond, you're signing up for two types of payments: coupon payments, which pay you interest, and a principal payment, which gives you the face value of the bond when the bond matures. Like stocks, bonds can be bought and sold at prices different than what they were issued for. For example, if interest rates fall, the prices on bonds increase. The yield to maturity (YTM) of a bond measures the rate of return over the remaining time before the bond matures based on the bond's current price, coupon payments and time remaining before the bond matures. If you have a target rate of return that you wish to achieve, plug that in as the yield to maturity to find the fair price of the bond you're willing to pay.

Calculate the annual coupon payments made on the bond by multiplying the face value of the bond by the stated interest rate. For example, if the bond pays a stated interest rate of 6 percent and has a face value of \$500, the annual coupon payments equal \$30.

Divide the yield to maturity by the number of coupon payments per year to find the periodic rate. For example, say you expect a 8-percent yield to maturity, and the bond makes semiannual coupon payments. Divide 0.08 by 2 to get 0.04 as the periodic rate.

Calculate the number of coupon payments remaining by multiplying the number of payments per year by the number of years until the bond matures. In this example, if the bond matures in eight years, multiply eight years by two payments per year to get 16 payments remaining.

Add 1 to the periodic yield to maturity rate. In this example, add 1 to 0.04 to get 1.04.

Raise the result to the power of the number of coupon payments remaining. In this example, raise 1.04 to the 16th power to get 1.872981246.

Divide 1 by the result. In this example, divide 1 by 1.872981246 to get 0.533908176.

Subtract the result from 1. In this example, subtract 0.533908176 from 1 to get 0.466091824.

Multiply the result by the coupon payment. Continuing the example, multiply 0.466091824 by \$30 to get \$13.98275473.

Divide the result by the desired yield to maturity to find the present value of the remaining coupon payments. The present value is what the future payments are worth in today's dollars. Furthering the example, divide 13.98275473 by 0.08 to get \$174.7844341.

Divide the face value of the bond by the Step 5 result to find the present value of the repayment of the principal at maturity. In this example, divide \$500 by 1.872981246 to get \$266.9540878.

Add the present value of the remaining coupon payments to the future value of the repayment of principal at maturity to find the fair market value of the bond. Finishing the example, add \$174.7844341 to \$266.9540878 to find the bond is worth \$441.74.

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